2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64662We show that $\mathfrak{aff}(n)$, the Lie algebra of affine transformations of ${\mathbb R}^n,$ is formally and analytically nondegenerate in the sense of A. Weinstein. This means that every analytic (resp., formal) Poisson structure vanishing at a point with a linear part corresponding to $\mathfrak{aff}(n)$ is locally analytically (resp., formally) linearizable.Some typos corrected. To appear in CRAS ParisSymplectic GeometryDifferential Geometrytext